Grid Design and Scale up of Geological Heterogeneity

Geological heterogeneity is often represented by assigning rock properties to grids of different block size. Some geological features are represented as discrete objects at the chosen grid block size and others are represented as continuous properties. There is a transition between the discrete and continuous where the size of the features is too small to be represented discretely and too large to be represented continuously. This is linked to the notion of REV, that is, it is impossible to choose a grid size where geological features are at REV scale. An extended view of modeling regimes is proposed by modifying the classical REV plot presented by Bear. The challenge of geostatistical modeling in transition regime is addressed. A continuous framework is considered with particular attention to the spatial continuity since the scale of variability is larger than the scale of modeling. Numerical experiments are conducted on various geological models.